Question

Two cross roads, each of width $10$ m, cut at right angles through the centre of a rectangular park of length $700$ m and breadth $300$ m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.

Answer 1

Hint: From figure we can say that , $PQ=10$m and $PS=300$m, $EH=10$m and $EF=700$m and also, $KL=10$m and $KN=10$m. Also, to find the area of roads and areas of $PQRS$ and $EFGH$. After that subtract the area of $KLMN$. For area of park excluding cross roads subtract area of roads from area of park.

Complete step-by-step answer:
Here from the figure we can say that, $PQ=10$m and $PS=300$m, $EH=10$m and $EF=700$m and also, $KL=10$m and $KN=10$m.
We can see in figure that,
Area of roads$=$ Area of $PQRS$$+$Area of $EFGH$$-$ Area of $KLMN$ ……… (1)
Since $KLMN$ is taken twice, which is to be subtracted.
Now $PQRS$ and $EFGH$is a rectangle.
Also, $KLMN$ is a square.
Now,
Area of $PQRS$$=PQ\times PS=300\times 10$
Simplifying we get,
Area of $PQRS$$=3000$sq. m ……… (2)
Now, area of $EFGH$$=EH\times EF=700\times 10$
Area of $EFGH$$=7000$sq. m ………… (3)
Also, area of $KLMN$$=KL\times KN=10\times 10$
area of $KLMN$$=100$sq. m …………. (4)
Now from (1), (2), (3) and (4),
Area of roads$=$$3000+7000-100$
Simplifying in simple form we get,
Area of roads $=$$9900$sq. m
Now we know that, $1$sq. m$=\dfrac{1}{10000}$ hectares.
So, we have an area of roads as $9900$sq. m.
$9900$sq. m$=\dfrac{9900}{10000}=0.99$ hectares.
Now, Area of park excluding cross roads $=$ Area of park $-$ Area of road.
Area of park excluding cross roads $=$ $(AB\times AD)-9900$
Now, in figure we can see that, $AB=EF$ and $AD=PS$.
Area of park excluding cross roads $=$ $(700\times 300)-9900$
Simplifying in simple form we get,
Area of park excluding cross roads $=$ $210000-9900$
Area of park excluding cross roads $=$ $200100$sq. m
Now in hectares, $200100$sq. m$=\dfrac{200100}{10000}=20.01$ hectares.
Therefore, Area of park excluding cross roads is $20.01$ hectares.

Note: Basically we have used, Area of roads$=$ Area of $PQRS$$+$Area of $EFGH$$-$ Area of $KLMN$ and Area of park excluding cross roads $=$ Area of park $-$ Area of road. Also, it should be clear that $1$sq. m$=\dfrac{1}{10000}$ hectares.